Details

sample108.0ms

Algorithm

intervals

Results

30.0ms	195×	body	80	valid
16.0ms	34×	body	1280	valid
10.0ms	18×	body	2560	valid
10.0ms	107×	body	80	nan
5.0ms	13×	body	640	valid
2.0ms	9×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	160	valid

simplify205.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	97
7	97
6	96
5	94
4	86
3	71
2	42
1	24
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) (* 2.0 a))
0.8b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
1.0b	(- (* b b) (* (* c a) 4.0))
21.8b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 72

Calls

4 calls:

173.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) (* 2.0 a))
84.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
16.0ms	(- (* b b) (* (* c a) 4.0))
27.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) (* 2.0 a))
150.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
85.0ms	(- (* b b) (* (* c a) 4.0))
142.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.5s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1313
1	399
0	154

prune826.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* c a) 4.0))) b)))
0.8b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
1.0b	(- (* b b) (* (* c a) 4.0))
21.8b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
47×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 118

Calls

4 calls:

129.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* c a) 4.0))) b)))
88.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
16.0ms	(- (* b b) (* (* c a) 4.0))
17.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series704.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* c a) 4.0))) b)))
149.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
84.0ms	(- (* b b) (* (* c a) 4.0))
136.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify3.2s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1854
1	556
0	220

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (* 2.0 a)) (/ 1 (- (sqrt (- (* b b) (* (* c a) 4.0))) b)))
0.8b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
1.0b	(- (* b b) (* (* c a) 4.0))
21.8b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

387×	`times-frac`
236×	`add-sqr-sqrt`
185×	`*-un-lft-identity`
135×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`div-exp`
50×	`difference-of-squares`
34×	`div-inv`
28×	`sqrt-prod`
25×	`add-cbrt-cube` `distribute-lft-out--`
24×	`associate-/r*`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
11×	`flip3--` `flip--`
8×	`add-log-exp`
7×	`associate-/l*`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log` `cbrt-unprod`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 287

Calls

4 calls:

146.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (sqrt (- (* b b) (* (* c a) 4.0))) b)))
80.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
14.0ms	(- (* b b) (* (* c a) 4.0))
16.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series708.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (sqrt (- (* b b) (* (* c a) 4.0))) b)))
160.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
97.0ms	(- (* b b) (* (* c a) 4.0))
139.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify4.4s

Counts

299 → 299

Iterations

Iter	Nodes
done	5043
2	3146
1	1273
0	430

prune2.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.9b

localize82.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* c a) 4.0))
1.0b	(- (* b b) (* (* c a) 4.0))
21.8b	(sqrt (- (* b b) (* (* c a) 4.0)))
21.8b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

16.0ms	(- (* b b) (* (* c a) 4.0))
16.0ms	(- (* b b) (* (* c a) 4.0))
19.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
27.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (* b b) (* (* c a) 4.0))
87.0ms	(- (* b b) (* (* c a) 4.0))
134.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
139.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify3.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	5003
3	2086
2	502
1	157
0	62

prune790.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

regimes580.0ms

Accuracy

82.1% (5.2b remaining)

Error of 10.7b against oracle of 5.5b and baseline of 34.7b

bsearch298.0ms

Steps

Iters	Range		Point
9	1.177766511972955e-157	7.998381519079639e-153	7.923524897992037e-153
6	-4.525167845450207e+100	-9.36795079059543e+99	-2.7668189408748547e+100

simplify36.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.2s	5755×	body	80	valid
1.2s	922×	body	1280	valid
965.0ms	1080×	body	2560	valid
461.0ms	2818×	body	80	nan
202.0ms	97×	body	5120	valid
196.0ms	483×	body	640	valid
71.0ms	238×	body	320	valid
22.0ms	117×	body	160	valid